Arbitrarily accurate twin composite $\pi$ pulse sequences

TL;DR

This paper introduces three classes of symmetric broadband composite pulse sequences with analytically derived phases, capable of arbitrarily high accuracy and flexible total pulse areas, outperforming previous sequences in robustness and adaptability.

Contribution

The authors develop new symmetric broadband composite pulse sequences with analytic phase formulas, enabling arbitrary accuracy and flexible pulse areas, advancing control in quantum systems.

Findings

Composite sequences are arbitrarily accurate with linear growth in error compensation.

Analytic formulas for phases are valid for any number of pulses.

Sequences outperform or match existing methods in robustness and flexibility.

Abstract

We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of $\pi$) valid for any number of constituent pulses. The transition probability is expressed by simple analytic formulas and the order of pulse area error compensation grows linearly with the number of pulses. Therefore, any desired compensation order can be produced by an appropriate composite sequence; in this sense, they are arbitrarily accurate. These composite pulses perform equally well or better than previously published ones. Moreover, the current sequences are more flexible as they allow total pulse areas of arbitrary integer multiples of $\pi$.